If a bus drives 3 km east, 5 km at 45° NE, 4 km at 20° NW, then 2 km south, what is the bus’s resultant displacement?
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Given : a bus drives 3 km east, 5 km at 45° ne, 4 km at 20° nw, then 2 km south,
To Find : bus's resultant displacement
Solution:
3 km east,
EAST = 3 km
5 km at 45° ne ( north East)
East = 5Cos45° = 5/√2 km = 3.54 km
North = 5Sin45° = 5/√2 km = 3.54 km
4 km at 20° nw ( north West )
West = 4Cos20° = 3.76 km = - 3.76 km EAST
North = 4Sin20° = 1.37 km
2 km south, = - 2 km North
NORTH = 3.54 + 1.37 - 3 = 2.91 km
EAST = 3 + 3.54 - 3.76 = 2.78 km
resultant displacement = √(2.91)² + (2.78)² = 4.02 km
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